Here are the links on the best peer-reviewed article that I'm aware of on trans women in elite women’s sports: https://blogs.bmj.com/medical-ethics/2019/08/12/transwomen-in-elite-womens-sport-clarifying-the-nuances-of-our-approach/ and https://www.sciencedaily.com/releases/2019/07/190723092111.htm. I believe that balancing everyone's rights is like saying, let's divide the cake more evenly. Why don't we also grow the cake at the same time? I know, I'm a capitalist...
I believe that gender (as opposed to self-identity and expression) is a manifestation of sex, but not every trans person subscribes to this view. The activists especially don't subscribe to this view because it's too nuanced for them - apparently gender is a social construct but gender is innate as well. Forget about the activists actually, trans people don't always reach consensus on trans issues.
I don't think the "gender is innate" narrative is helpful in explaining trans people to cis people. I too must say, I do not understand why you don't "feel like" a woman. I'd say that comes down to never having experienced male-to-female dysphoria, but I can't speak for your non-dysphoria experience, just as you won't be able to speak for my dysphoria experience. I think it's just better for people to accept that everyone has different life experiences, and that it's not helpful to make assumptions about life experiences not lived all-round.
I believe there is a difference between gender, gender identity and gender expression - gender is the socially-negotiated manifestation of sex, gender identity is self-identification, and it's gender expression that's socially constructed: https://medium.com/@danapham.au/the-social-negotiation-of-gender-identity-and-pronouns-9ad362059334. Dysphoria relates to gender moreso than identity and expression, and has more scientific grounding. Hopefully you can now see why I'm not well-liked by the wokes, and how much they've butchered the traditional trans narrative, eg Gender Recognition Act 2004, which apparently is now here to stay: https://www.bbc.com/news/uk-politics-54246686.
Here are my views on trans children: https://medium.com/@danapham.au/the-australian-christian-lobby-does-not-understand-trans-issues-5ed10b144041.
For what it's worth, I'm a gender egalitarian, not a feminist. And I think both of sides of the debate kinda ignore the fact that gender is a socially-negotiated (not determined) manifestation of sex, which makes it different to self-identification and expression. Dating preferences with respect to trans people, or anyone else for that matter, is not bigotry. We may agree on more than we realise :)